With the right wheels, that tire should clear fine. However, you may run into issues finding the proper wheel to work with that size tire in an 8 lug pattern. A 31x10.50x15 tire will require a 7" wide wheel at the minimum, 8" would be preferred. Finding a wheel that size in 6 lug is fairly easy, as GM used them on 1/2 ton 4x4s for many years. But in an 8 lug, you would have to look for aftermarket or custom made wheels.
You also make mention of being able to drive in snow, without having 4wd, a wide floatation tire like the 31x10.50 isn't the best choice. A tall, narrow tire would perform much better. I would suggest looking into a 16x7 wheel, with 3 to 3.5 inch backspacing, and using a 215/85/16 or 235/85/16 tire. Either will help with the rad speed issue, and will also give you the snow performance.
